{"date_updated":"2021-01-12T06:48:54Z","page":"627 - 644","publication_status":"published","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","title":"Algebraic vertices of non-convex polyhedra","year":"2017","month":"02","language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2016.12.026","quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"intvolume":" 308","department":[{"_id":"HeEd"}],"volume":308,"oa_version":"Submitted Version","publication_identifier":{"issn":["00018708"]},"scopus_import":1,"status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1508.07594","open_access":"1"}],"type":"journal_article","author":[{"first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Imre","last_name":"Bárány","full_name":"Bárány, Imre"},{"last_name":"Robins","first_name":"Sinai","full_name":"Robins, Sinai"}],"abstract":[{"lang":"eng","text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform."}],"oa":1,"publication":"Advances in Mathematics","date_published":"2017-02-21T00:00:00Z","date_created":"2018-12-11T11:50:34Z","_id":"1180","publisher":"Academic Press","citation":{"chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” *Advances in Mathematics*. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.","ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. *Advances in Mathematics*. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026","ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644.","mla":"Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” *Advances in Mathematics*, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.","apa":"Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. *Advances in Mathematics*. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026","ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” *Advances in Mathematics*, vol. 308. Academic Press, pp. 627–644, 2017.","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644."},"day":"21","publist_id":"6173","ec_funded":1}